Combining Texts

All the ideas for 'Taking Rights Seriously', 'The Sentiment of Rationality' and 'Higher-Order Logic'

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33 ideas

1. Philosophy / A. Wisdom / 1. Nature of Wisdom
22659 It is wisdom to believe what you desire, because belief is needed to achieve it [James]
1. Philosophy / D. Nature of Philosophy / 1. Philosophy
22657 All good philosophers start from a dumb conviction about which truths can be revealed [James]
1. Philosophy / E. Nature of Metaphysics / 3. Metaphysical Systems
22647 A complete system is just a classification of the whole world's ingredients [James]
2. Reason / A. Nature of Reason / 5. Objectivity
22648 A single explanation must have a single point of view [James]
2. Reason / B. Laws of Thought / 6. Ockham's Razor
22644 Our greatest pleasure is the economy of reducing chaotic facts to one single fact [James]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
10301 The axiom of choice is controversial, but it could be replaced [Shapiro]
5. Theory of Logic / A. Overview of Logic / 5. First-Order Logic
10588 First-order logic is Complete, and Compact, with the Löwenheim-Skolem Theorems [Shapiro]
5. Theory of Logic / A. Overview of Logic / 7. Second-Order Logic
10298 Some say that second-order logic is mathematics, not logic [Shapiro]
10299 If the aim of logic is to codify inferences, second-order logic is useless [Shapiro]
5. Theory of Logic / B. Logical Consequence / 1. Logical Consequence
10300 Logical consequence can be defined in terms of the logical terminology [Shapiro]
5. Theory of Logic / G. Quantification / 5. Second-Order Quantification
10290 Second-order variables also range over properties, sets, relations or functions [Shapiro]
5. Theory of Logic / J. Model Theory in Logic / 3. Löwenheim-Skolem Theorems
10590 Up Löwenheim-Skolem: if natural numbers satisfy wffs, then an infinite domain satisfies them [Shapiro]
10296 The Löwenheim-Skolem Theorems fail for second-order languages with standard semantics [Shapiro]
10297 The Löwenheim-Skolem theorem seems to be a defect of first-order logic [Shapiro]
10292 Downward Löwenheim-Skolem: if there's an infinite model, there is a countable model [Shapiro]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / e. Peano arithmetic 2nd-order
10294 Second-order logic has the expressive power for mathematics, but an unworkable model theory [Shapiro]
7. Existence / E. Categories / 2. Categorisation
22649 Classification can only ever be for a particular purpose [James]
8. Modes of Existence / B. Properties / 11. Properties as Sets
10591 Logicians use 'property' and 'set' interchangeably, with little hanging on it [Shapiro]
14. Science / A. Basis of Science / 1. Observation
22655 Scientific genius extracts more than other people from the same evidence [James]
14. Science / A. Basis of Science / 6. Falsification
22658 Experimenters assume the theory is true, and stick to it as long as result don't disappoint [James]
14. Science / C. Induction / 3. Limits of Induction
22654 We can't know if the laws of nature are stable, but we must postulate it or assume it [James]
14. Science / C. Induction / 6. Bayes's Theorem
22656 Trying to assess probabilities by mere calculation is absurd and impossible [James]
14. Science / D. Explanation / 2. Types of Explanation / j. Explanations by reduction
22646 We have a passion for knowing the parts of something, rather than the whole [James]
15. Nature of Minds / A. Nature of Mind / 1. Mind / b. Purpose of mind
22652 The mind has evolved entirely for practical interests, seen in our reflex actions [James]
15. Nature of Minds / A. Nature of Mind / 7. Animal Minds
22651 Dogs' curiosity only concerns what will happen next [James]
18. Thought / A. Modes of Thought / 5. Rationality / a. Rationality
22650 How can the ground of rationality be itself rational? [James]
18. Thought / A. Modes of Thought / 5. Rationality / b. Human rationality
22643 It seems that we feel rational when we detect no irrationality [James]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / d. Biological ethics
22660 Evolution suggests prevailing or survival as a new criterion of right and wrong [James]
24. Political Theory / D. Ideologies / 6. Liberalism / b. Liberal individualism
23104 Dworkin believed we should promote equality, to increase autonomy [Dworkin, by Kekes]
25. Social Practice / B. Equalities / 1. Grounds of equality
23257 We can treat people as equals, or actually treat them equally [Dworkin, by Grayling]
18621 Treating people as equals is the one basic value of all plausible political theories [Dworkin, by Kymlicka]
26. Natural Theory / C. Causation / 8. Particular Causation / d. Selecting the cause
22645 Understanding by means of causes is useless if they are not reduced to a minimum number [James]
29. Religion / B. Monotheistic Religion / 4. Christianity / a. Christianity
22653 Early Christianity says God recognises the neglected weak and tender impulses [James]